This Wikipedia article says it comes from marketing and advertising, but I first remember seeing the term used to describe signatures on posts made on the dial-up bulletin board systems (BBS) that predated general Internet usage. Because of the cost of dial-up service, especially long-distance calls, long signatures were discouraged and shorter taglines encouraged.

I checked Wiki, too. And I get you. Unfortunately I did not
have a computer back in the dial up days, but I've heard
plenty of horror stories. So the "tagline" signature
thing makes sense. \\
There are days when I think I still live in that day, however,
but I am so impatient, I can hardly imagine what it
used to be like. Just waiting some mornings for my
unit to start up seems an eternity. Even being retired
with tons of time on my hands it is a long wait.

So my "Please, draw me a sheep", is a tagline? Even when
it really is just a favorite phrase, and really does not
say a lot about me personally???

You've changed yours since I first joined this site. Does the
tagline just represent a current mood, e.g.?

So true.
I've been to funerals of a boy (8 years),cancer. Saddest
was for a fifth grade boy - had been sitting on the
corn loader following the combine. He fell in and the corn
buried him. No one knew where he was, but found three
days later when the corn was taken to the elevator.
Denied to many. Cherish each minute: one day at a time.